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Question

If the ratio of area of triangle inscribed in the ellipse x2a2+y2b2=1 to that of triangle formed by the corresponding points on the auxiliary circle is 12, then the eccentricity of the ellipse is

A
12
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B
13
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C
32
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D
12
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Solution

The correct option is C 32
The ratio of area of any triangle inscribed in an ellipse to the area of triangle formed by corresponding points on the auxiliary circle is equal to the ratio of semi-minor axis to semi major axis.
For ellipse x2a2+y2b2=1
Assume a>b. So,the given ratio is ba=12
Now e=1b2a2=114
e=32

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